Blind Community Detection From Low-Rank Excitations of a Graph Filter
Blind Community Detection From Low-Rank Excitations of a Graph Filter
复制标题
DOI：
10.1109/tsp.2019.2961296
复制
发表时间：
2018-09
影响因子：
5.4
通讯作者：
Hoi-To Wai;Santiago Segarra;A. Ozdaglar;A. Scaglione;A. Jadbabaie
中科院分区：
文献类型：
--
作者：
Hoi-To Wai;Santiago Segarra;A. Ozdaglar;A. Scaglione;A. Jadbabaie
本文考虑了一种新的框架，用于从图节点处的信号观测来检测图中的社区。我们将观测到的信号建模为一个未知网络过程的含噪输出，该网络过程表示为一个由一组未知低秩输入/激励所激发的图滤波器。这个模型的应用场景包括扩散动力学、定价实验和舆论动态。我们的目标不是学习图本身的精确参数，而是直接检索社区结构。本文表明，可以通过对图信号的协方差矩阵应用一种谱方法来检测社区。我们的分析表明，社区检测性能取决于图滤波器的一种内在“低通”特性。我们还表明，当潜在参数向量已知时，可以通过一种低秩矩阵加稀疏分解方法来提高性能。数值结果证明我们的方法是有效的。
This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on an intrinsic ‘low-pass’ property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical results demonstrate that our approach is effective.